A purring Grey is a real treat, but it's a rare occurrence. Allowing you to touch her like that indicates that Rebecca trusts you. Now, you mention that she tried to bite you, but you may be misinterpreting her beak action. When they take a bit of a swipe at you in the midst of scritching, it's usually more that they are telling you that you aren't doing it right. The "bite" is more like they are saying "hey!" rather than actually trying to bite you.
Our TAG frequently tries to "correct" my scritches. He will offer his head for a scratch, then pull away and scratch himself with his foot and offer his head again at a different angle in order to get scratched in a specific place. If I'm not paying attention, or I don't scratch hard/gently enough, or in the wrong place, he will take a swipe at me with his beak to indicate that he's a bit annoyed about my inattention or error in where he wants it. If I continue to do it wrong, or in the wrong place, he might give me a nip, but it's not very hard, just hard enough to get the point across. (Stupid monkeys! )
We are the ones being trained.
As for getting her back into her cage without upsetting her too much. Give her a treat to hold in her beak when you want her back in her cage. It will keep her mouth busy while you place her inside her cage.
Other methods include:
- placing a special treat inside the cage for her to go in after
- using a handheld perch to transfer her into her cage
- (at bedtime) lowering the lights and shutting off the TV/computer and making the room quiet and darker to indicate that it's bedtime
- giving her a toy to occupy her mouth during transfer
- making the cage her food station and not feeding her outside the cage
ALWAYS make going back in her cage worth her while.